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RELATIONS AND FUNCTIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSRELATIONS AND FUNCTIONS1 Mark
MCQ
The function f(x) = x - [x] has period of:
  • A
    1
  • ✓
    2
  • C
    3
✓

Answer

Correct option: B.
2
Let T is a positive real number.
Let f(x) is periodic with period T.
Now, f(x + T) = f(x), for all $\text{x} \in \text{R}$
⇒ x + T - [x + T] = x - [x], for all $ \text{x} \in \text{R}$
⇒ [x + T] - [x] = T, for all $ \text{x} \in \text{R}$
Thus, there exist T > 0 such that f(x + T) = f(x) for all $ \text{x} \in \text{R}$
Now, the smallest value of T satisfying f(x + T) = f(x) for all $ \text{x} \in \text{R}$ is 1
So, f(x) = x - [x] has period 1

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